There are many linear motion re-circulating ball bearing assemblies in the prior art. As an example in the Magee U.S. Pat. No. 3,545,826, there is described a self-aligning bearing which is particularly advantageous because it reduces the wear between the respective parts caused by binding of the shaft with respect to the balls. It is known that one of the primary causes of wear in linear ball bearing assemblies is related to the misalignment of the shaft with respect to the housing in which the linear bearing is placed. It is further known that linear motion recirculating ball bearings do not damp vibrations as well as conventional slideways. The self-alignment features are merely to reduce costs of manufacture particularly when multiple bushings are used to obtain high stiffness. A self-aligning bearing is disclosed in the McCloskey U.S. Pat. No. 3,893,732 which states that the resilient O-rings used for self-aligning may be sized to pre-load the bearing. No attempt, however, has been made to provide a successful damping or control of "radial deflection".